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Search: id:A140356
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| A140356 |
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Triangle T(n,m) read by rows: m! if m <= floor(n/2), and (n-m)! else. |
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+0
2
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| 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 6, 2, 1, 1, 1, 1, 2, 6, 6, 2, 1, 1, 1, 1, 2, 6, 24, 6, 2, 1, 1, 1, 1, 2, 6, 24, 24, 6, 2, 1, 1, 1, 1, 2, 6, 24, 120, 24, 6, 2, 1, 1, 1, 1, 2, 6, 24, 120, 120, 24, 6, 2, 1, 1, 1, 1, 2, 6, 24, 120, 720, 120, 24, 6, 2, 1, 1, 1, 1, 2, 6, 24
(list; table; graph; listen)
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OFFSET
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0,13
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COMMENT
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Row sums: 1, 2, 3, 4, 6, 8, 14, 20, 44, 68, 188,... which is
2*A003422((n+1)/2) if n is odd, and A003422(n/2)+A003422(1+n/2) if n is even.
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FORMULA
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T(n,m) = A000142(m) if m<=[n/2], = A000142(n-m) if m>[n/2], 0<=m<=n.
Conjecture: limit_{n->infinity} sum_{m=0..n} ( 1/binomial(n,m) - T(n,m) ) = 0.
T(n,m) = T(n,n-m).
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EXAMPLE
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1,
1, 1,
1, 1, 1,
1, 1, 1, 1,
1, 1, 2, 1, 1,
1, 1, 2, 2, 1, 1,
1, 1, 2, 6, 2, 1, 1,
1, 1, 2, 6, 6, 2, 1, 1,
1, 1, 2, 6, 24, 6, 2, 1,1,
1, 1, 2, 6, 24, 24, 6, 2, 1, 1,
1, 1, 2, 6, 24, 120, 24, 6, 2, 1, 1
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MATHEMATICA
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g[n_, m_] := If[m <= Floor[n/2], m!, (n - m)! ]; w = Table[Table[g[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[w] Table[Apply[Plus, Table[g[n, m], {m, 0, n}]], {n, 0, 10}]
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CROSSREFS
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Sequence in context: A139147 A055801 A155050 this_sequence A119963 A057790 A052307
Adjacent sequences: A140353 A140354 A140355 this_sequence A140357 A140358 A140359
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KEYWORD
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nonn,easy,tabl,new
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), May 30 2008
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EXTENSIONS
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Non-Ascii characters corrected, offset set to 0, reported Mma experiments removed - The Assoc. Eds. of the OEIS, Oct 31 2009
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